This is maybe obvious, but in case it isn’t, we’re now in the Iron Age so the arrows are probably tipped by iron points instead of bronze. And the swords are now either iron or a crude form of steel. But do note, these folks don’t know they’re in the Iron Age. They’re just adapting to the technologies that are driving their economy. So they wouldn’t have stopped using bronze for some applications. Nor would it particularly matter to them which they were using if it did the job they expected of it.
But on this score the Israelites and the Jeudeans have a little edge b/c they’ve been dealing with the Philistines for years. And those bad boys were some of the first to develop and introduce iron-based technology and weaponry.
As far as the arrow tips themselves are concerned, it wouldn’t be a huge advantage to be iron vs bronze. Swords, yes, but not arrows. The advantage would be in having ready sources for your needs nearby and not having to depend on your freinimies to supply it. Which was the case with the NK. If I remember correctly, that’s one of the reasons the North kept the south subjugated. They were the ones with the iron reserves.
And there’s another thing some of your garrison soldiers would be doing – making and caring for weapons and horses and provisioning themselves and the mounts and so on. And some would be specialists in stuff like making and fletching arrows or scabbards or shields etc. And there would have to have been cart wrights and smitthies amongst them as well.
And Ahab being the sharp king that he is, every week some would be on rotating patrols; they would also be the pony express running or riding messages to the key forts around the kingdom. Some guards and patrols would be on duty around the capital around the clock (if there were clocks); some patrolling out in the hinterlands, and especially some on the border. One of the things Omri would have drilled into Ahab was to always know what was going on on your borders. So Ahab and O probably knew of the Damascene movements about as soon as they formed up. That’s how you keep a little kingdom powerful and relevant.